
theorem A265:
  for n be Nat, f be complex-valued XFinSequence st
    n in dom f holds XProduct (f|n) * f.n = XProduct (f|(n+1))
  proof
    let n be Nat, f be complex-valued XFinSequence;
    assume A1: n in dom f;
    reconsider f1 = f as XFinSequence of COMPLEX;
    multcomplex.(multcomplex "**" f|n, f.n) = multcomplex "**" f|(n+1)
      by A1,AFINSQ_2:43;
    hence thesis by BINOP_2:def 5;
  end;
